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java.lang.Objectpapaya.Eigenvalue
public class Eigenvalue
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
Shamelessly copied (and modified) from the
JAMA Java
Matrix package. To make things compatible with how most users use Processing, the
class take in float matrices. However, to preserve the acccuracy of the computations, the algorithm
first casts the input into a double array, prior to doing anything. All methods also return doubles; Use
Cast.doubleToFloat(double[][])
if you want/need to cast everything back to floats for
further (non-high-accuracy-dependant) processing (pun intended).
Constructor Summary | |
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Eigenvalue(float[][] Arg)
Check for symmetry, then construct the eigenvalue decomposition. |
Method Summary | |
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double[][] |
getD()
Return the block diagonal eigenvalue matrix |
double[] |
getImagEigenvalues()
Return the imaginary parts of the eigenvalues |
double[] |
getRealEigenvalues()
Return the real parts of the eigenvalues |
double[][] |
getV()
Return the eigenvector matrix with each column corresponding to an eigenvector of the input matrix. |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public Eigenvalue(float[][] Arg)
getV()
,
getD()
,
getRealEigenvalues()
,
getImagEigenvalues()
Method Detail |
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public double[][] getV()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public double[][] getD()
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